Problem: Rewrite as a simplified fraction. ${0.64\overline{3} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 643.3333...\\ 100x &= 64.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 579}$ ${x = \dfrac{579}{900}} $ ${x = \dfrac{193}{300}} $